Artificial neural networks (hereinafter “neural networks”) are useful for a range of problems. For example, some modeling techniques use deep neural network (DNN) models, e.g., neural networks with multiple hidden layers, for modeling the semantic meaning of text strings. DNN models can outperform semantic modeling techniques that use conventional topic models or latent semantic analysis (LSA) models. However, conventional DNNs are limited in the range of problems for which they can be used.